PhD defence of Mahmood Mohammed - On route to infinite gain CMOS Operational Transconductance Amplifiers and its impact on speed and capacitive load drivability of closed-loop analog applications
This thesis introduces a many-stage CMOS Operational Transconductance Amplifiers (OTAs) design technique that allows cascading identical gain stages (for arbitrarily scalable ultra-high DC gain) while driving an ultra-wide range of capacitive loads (CLs). At the heart of the proposed design technique, is a new generalized theory on the relationship between frequency response and settling time of CMOS OTAs in the presence of Pole-Zero (P-Z) pairs (or doublets). Interestingly, the presence of P-Z pairs/doublets in the open-loop frequency response of CMOS OTAs has always been considered detrimental to the closed-loop operation of CMOS OTAs. However, the new proposed theory is showing how to reduce the impact of such P-Z pairs on the closed-loop operation of CMOS OTAs - using low-frequency zeros and cascaded-gain stages – consequently revealing untapped opportunities for many-stage CMOS OTA design. The proposed scalable design of the many-stage CMOS OTA ensures stability, when configured in closed loop, by means of a new frequency compensation technique that relies on low-frequency left-half-plane zeros to allow the proposed OTA to operate for a desired closed-loop behavior. The proposed design realizes a CMOS OTA with scalable-gain that increases in 25 dB increments per stage, achieving a total gain from 50 dB to 200 dB for a 2-stage to an 8-stage configuration, respectively. The design is verified through extensive simulations based on a standard TSMC 65 nm CMOS process. Also, as a proof-of-concept, the design has been validated by fabricating 2-, 3-, and 4-stage CMOS OTAs, and the measurement results show that the 2-stage OTA is achieving a DC gain of 50 dB with a CL-drivability ratio of 10,000x, the 3- stage OTA is achieving a DC gain of 70 dB with a CL-drivability of 1,000,000x, and the 4-stage OTA is achieving a DC gain of 90 dB with a CL-drivability of 1,000,000x. This is a 10-to-1000- time improvement in the state-of-the-art.